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A person needs at least 20kPa *from the mask to breathe*. Not 20kPa *ambient pressure*. Please learn to read.

The mask pressure must match the ambient pressure, or else the wearer's lungs will rupture (unless they're wearing an enclosed pressure suit). Please learn physics. Again, this is the reason for the 40,000ft flight ceiling for commercial aircraft; oxygen masks rapidly lose their effectiveness with an ambient pressure below 0.2atm, which is why pressure suits are required for pilots flying at higher altitudes. The absolute physical limit for unpressurized flight is known as the Armstrong Limit, which occurs at about 62,000 ft; even wearing an oxygen mask, your bodily fluids will start to boil above that altitude.

The "problematic loading on the capsules" is from the high speed aerodynamics, not the ambient pressure

Aerodynamic loading = pressure. If you have high loadings, you have high pressures. Period.

The high loadings are from high _variations_ in pressure. The average pressure around the capsule is still equal to the ambient pressure. Leaks in the passenger compartment are almost certainly side-facing, so the capsule will equalize to the pressure of the air on the sides of the capsule (which will be close to ambient or likely below, due to the Bernoulli principle), not the higher pressure in front. And note that the variations in pressure don't have to be very high to cause serious buffeting. The Hyperloop capsule masses 15000kg, with a frontal cross-section of about 2 m^2. Applying an extra 1atm to the front of the capsule will decelerate it faster than 1g. If the air beneath the capsule transiently becomes about 0.03atm higher density than the air above (due to turbulence or ground effect), it will lift the entire capsule off the track. This is the worrisome high-speed aerodynamics I was talking about.

Wait, meaning that while it's technically possible, but it'd be really tricky to accomplish? Gee, I wish I had written something like "Branching would be really tricky, but there's no physical barriers" at the top of my post;)

Well, there are physical barriers to a static design that allows branching. Actively moving an entire section of tube to reconnect it to a new one is sort of a brute-force approach, and highly unlikely that it would be worth the complexity and risk, in my opinion at least.

Drag is reduced in the first place by using hydrogen even at a given pressure. And you can use 1/4th the pressure and still maintain lift because you're moving four times as fast. And given how few reboosts are needed from LA to SF in the base case, a few more per unit distance hardly seems limiting.

1/4th the pressure is still problematic, because what do you do while you're accelerating up to speed? You'd have to use pressurized onboard gas to levitate with, which would then require more vacuum pumping with every run. The Alpha design uses wheels for "taxiing" at low speeds; it's unclear at what speed the compressor is able to provide all of the needed lift.

If you consider that the steel Hyperloop pipe draped across 30m-spaced pylons will approximate a vertical sine wave, then at 700mph the allowable sag is only about 5cm

Irrelevant because earthquakes impose far more deflection that you have to be able to counter (and that the proposal calls for countering) than a craft moving past.

Relevant because the problem is the frequency, not the amplitude. Large earthquakes tend to cause much lower-frequency deflections, which are far easier to deal with, even if the amplitude is higher. The problem I described has to do with the static height profile of the tube, not the effect of the passing capsule distorting it (which is negligible). Even if the skis (on springs) can accelerate at 10g's to maintain contact with the tube surface, then a 5cm oscillation with 30m wavelength is sufficient to cause the skis to completely lift off the surface of the tube after each pylon, causing a very jarring ride. A low-frequency earthquake deflection on the other hand, say with 200m wavelength, could not realistically have high enough amplitude to cause the skis to skip like this. Of course, if you have the bad luck to be riding the hyperloop straight over the epicenter when the earthquake lets loose, then there will be high-amplitude earthquake waves of all frequencies and all bets are off.

Mechanical braking from 1500mph in the event of an emergency is also a non-starter

The Alpha proposal calls for a "mechanical braking system"; I agree that magnetic brakes would be preferable in principle, though at Hyperloop speeds there's enough kinetic energy involved that the capsule component of the brakes would likely melt from the induced current. Permanent magnets on the capsule would probably be too heavy. And magnets/electromagnets on 350 linear miles of tube would likely be too costly/complicated. So unless there's a way to have the electromagnet component on the capsule, but make sure that nearly all the heat is dissipated in the steel tube and not the capsule, I'm not sure it would be workable. I have similar concerns about the aluminum capsule rotor, and whether it might become problematically hot during the linear acceleration/deceleration phase. A solid aluminum rotor could absorb the electromagnetically induced waste heat from 0-700mph acceleration without melting (by a factor of about 2), but the Alpha design calls for it to be hollow. And accelerating to 1500mph involves >4x the energy of 700mph.

a 700mph capsule will incur about 2g's of aerobraking deceleration

Where are you getting this from? Even if the tube was instantly full pressure (which it wouldn't be), a streamlined shape will not experience 2Gs at 700mph, any more than a passenger jet losing full engine power does. And anyway, 10g horizontal is not fatal even if that was the case. The average untrained individual, properly restrained, can tolerate 10g for a minute without even loss of cognitive function.

According to High-G training, untrained individuals tend to black out between 4 and 6 g's. (Then a few sentences later it says that one minute at 15g's could be deadly, then a few sentences after that says that several minutes at 17g's is ok. Go figure.) In any case, streamlined passenger jets are not traveling 700mph in 1atm; more like 550mph in 0.2atm. And the Hyperloop capsule is emphatically NOT streamlined; it has a honking circular front cross-section with a giant compressor on it, designed for very low-pressure input, which would immediately stop working if the pressure spikes up. Subjecting the entire Hyperloop capsule shape suddenly to 1atm, in a tube not much bigger than it is, would result in tremendous aerodynamic drag.

Clever, but probably unworkable given the large cross-section of the capsule relative to the tube. Even on a perfectly straight track (no banking), taking the upper branch would require the skis to "split" wide enough that the entire capsule width would fit between them. Given the Alpha design numbers (ski width 0.9m, tube diameter 2.23m, capsule width 1.34m), the skis would have to split nearly horizontal to avoid the lower-branch "gap", and it's unlikely they could function at such a steep angle. Maintaining the precise shape of a non-circular tube against vacuum pressure is also a very difficult problem.

And the advantage [of hydrogen] is being able to travel at mach freaking 4, not about the reduction of drag at a given speed (which is, FYI, true also).

Making the Hyperloop go that fast would require an impossibly straight and level track. Even at the Hyperloop's current design speed (Mach 0.99), the maximum allowable vertical sag of the tube between 30m-spaced pillars is only about 5cm. Any more than that, and the air ski suspension won't be able to compensate and the capsule will start skipping and bouncing. At Mach 3-4, the tube couldn't sag more than a few millimeters between pylons before overwhelming the suspension. So for the foreseeable future, the advantage of hydrogen will be that it reduces the problem of choked flow and the Kantrowitz limit at more reasonable (~700mph) speeds. By the time the Hyperloop is commonplace and we're contemplating Mach 4 travel, we'll probably be talking fully evacuated tubes with maglev like ET3. Maglev could probably also deal more flexibly with uneven track height at those speeds. Or Musk could be right in thinking that supersonic air travel is ultimately the best solution for >1000km distances.

Most people will black out if the oxygen partial pressure drops below about 14kPa. A highly conditioned athlete or acclimatized mountain climber could stay conscious with 10kPa for a short time. 7kPa O2 is equivalent to the summit of Everest without an oxygen tank; very few people can survive that for any length of time.

The "problematic loading on the capsules" is from the high speed aerodynamics, not the ambient pressure. The question is whether you can simultaneously get the ambient pressure high enough that the passengers don't suffocate, while keeping the aerodynamic forces low enough that the capsule doesn't disintegrate. This seems to be possible with a 700mph Hyperloop, but probably impossible with a 1500mph Hyperloop.

The main advantage to hydrogen would be overcoming the Kantrowitz choking effect caused by supersonic flow;

Yes, understood, and any design choice that further lowers the density of gas in the tube requires more compressor work for the air bearings, which require a fixed mass per second flow.

I don't think that's right. The air bearings function based on pressure, not mass density. 50Pa air + 50Pa H2 would keep the overall tube pressure the same, so the compressors' job wouldn't change. In fact, since the H2 (in my proposed design) would be injected into the ski air stream post-compression, the compressors would have less work to do, not more. The required mass flow to the skis using an air/H2 mix would actually be substantially less than in the Alpha proposal. Again, the pressure is what's important (averaging 7kPa under the skis), not the mass per se.

That kind of deceleration assumes an instantaneous transition from 100 to 100000 Pa, which is not possible absent total destruction of the tube immediately prior to a pod at cruise, in which case deceleration due to air is moot. Otherwise the pressure in a 381 mile long tube must rise gradually.

Ok, let's look at an emergency scenario where a capsule (not the tube) undergoes rapid depressurization. To save the passengers, the ambient pressure in the entire tube must quickly (within a few seconds) be brought up to levels at which oxygen masks will function; about 20kPa. This can be done by flooding the tube with air evenly along its length; no tube destruction required. The question is whether a 20kPa tube atmosphere would impose problematic aerobraking forces on the capsules. At 700mph, you'd probably be ok. But at 1500mph, you'd immediately be exceeding the ambient speed of sound, which would be very bad. (Flooding the tube with a high H2 mixture to keep the speed of sound high would create a very explosive environment, so that's not an option.)

Long story short: if your capsule suddenly depressurizes at 1500mph, you're dead. But at 700mph, you might still be ok. The risks and complexities associated with hypersonic tube travel seem to outweigh the benefits, at least for now. Subsonic is good enough, really.

Keep in mind that these quotes are all excerpted from articles by bloggers, not engineers. The skis connect to the capsule through a hefty suspension, so minor bumps won't be transmitted to the passenger compartment. There will be no lateral acceleration experienced by passengers; the capsule would bank freely like a bobsled, so all banking acceleration will be perceived as vertical (as in an airplane), pressing you down into your reclined seat, thus much less barf-inducing. The noise levels shouldn't be problematic, since the ducted/bypassed air is still at extremely low pressure (2kPa, equivalent to 30km/90,000ft altitude), and can be sonically isolated from the cabin. The airflow around the exterior of the capsule is vanishingly thin, so it should produce hardly any noise at all.

The main advantage to hydrogen would be overcoming the Kantrowitz choking effect caused by supersonic flow; this is one of the most significant design constraints of the Hyperloop. Increasing the speed of sound (by mixing the air with hydrogen) increases the speed at which the ambient gas can flow around the capsule, greatly reducing the pressure that builds up in front at a given speed. Hydrogen is cheap; liquid hydrogen can be had for less than $1/kg, so cost is a non-issue.

Another design constraint of the Hyperloop is cooling the compressed ski air. The Alpha design calls for a 300kg water tank and intercooler, flash-heating the water to steam and storing it in "steam tanks", the complications of which are swept under the rug. (300kg of water would become 500 m^3 of steam at 1atm, several times the volume of the capsule itself.) By injecting liquid H2 into the air stream to cool it, the need for the intercooler and steam tanks would go away. Hydrogen has an exceptionally high specific heat; liquid hydrogen is extremely effective at removing heat from a system. Some of the compressed air + H2 could be further compressed and stored onboard the capsule to maintain the tube at 100Pa, or perhaps the excess H2 could be handled by placing adsorbent material (e.g. activated charcoal) in the tube to soak it up, and replacing/recharging this material at intervals. Since hydrogen moves so fast, placing the adsorbent material only at the endpoints might be sufficient.

The stopping distance is just fine. At 30 second intervals at full speed, the distance between capsules is about 10km. A 1g deceleration (combined force = 1.4g, equivalent to pressing hard on car brakes) will stop the capsule in less than 6km. No internal organ squishing required.

Passenger aircraft commonly bank at up to 30, which is a vertical g-force of 1.15g. The Tesla Model S P85D accelerates off the line at 1G longitudinal, for a combined g-force of about 1.4g. The Gravitron (common at carnivals) pulls 3g's continuous. Roller coasters commonly pull 4-5g's for short times. (though admittedly, that can be barf-inducing.) The Hyperloop is designed for a maximum combined g-force of 1.4g, corresponding to a 45 banking angle. With reclining seats, this should feel similar to a Model S accelerating off the line, and should be easily tolerated. The key consideration will be to minimize "jerk"; abrupt changes in acceleration. So the curves will have to be designed so the banking radius changes gradually rather than abruptly.
No doubt there will be people who are intolerant of the Hyperloop, just as there are people who are phobic/intolerant of air travel. Perhaps there could be a designated "slow hour" where the capsules are run at 3/4 speed to reduce the g-forces. But with appropriate warning and visual feedback provided, I think most passengers would quickly get used to it.

But to travel at 800 mph without making your passengers sick and barfing, the route actually needs curves to be 16 times as smooth as the 200 mph CHSR.

The Hyperloop will bank freely like a bobsled; the passengers will experience virtually no lateral acceleration. (The same is true of an airplane in a tight bank.) This will make the ride far less barf-inducing. The lack of turbulence will also help greatly.

The Hyperloop skis will be on a flexible suspension; the pylons can sway many centimeters (e.g. in earthquakes) before the ride quality would be affected. In other words, the skis can move quite a lot to maintain precise contact with the tube, while the passenger compartment remains stable. The raw materials and basic construction will be the expensive part; polishing the interior to the required smoothness is comparatively trivial. The vacuum part is also fairly simple; the vast majority of the tube is simple continuous inch-thick steel, which is trivial to make airtight. The complexity will be at the endpoint stations and airlocks, but given that it's only a soft vacuum being maintained (100Pa), even this is easily manageable.

The hyperloop uses low pressure air because the design assumes there will always be lots of leaks, which can be overcome by the pumps. Air will always be leaking in, so you just pump it back out. And because it's not a vacuum, the pumps aren't as insane as they'd need to be to maintain a hard vacuum.

As soon as you start talking about putting anything but air in the thing, then that whole idea goes out the window, you now need to go from "mostly airtight" to "completely and utterly airtight", and everything gets incredibly difficult.

You could do a mixture of air with other gases, and gain many of the advantages while still avoiding a hard air vacuum. For instance, 50Pa air + 50Pa water vapor, or even 50Pa air + 50Pa H2. A promising approach would be for the capsules to store on board some of the air they're compressing anyway, to help maintain the tube pressure. The alternate gases could even be added as part of the cooling system; if liquid nitrogen or liquid hydrogen were injected directly into the compressed air stream to cool it, it would greatly reduce the need for water intercoolers and onboard steam storage, increase the available pressure to the skis, and be balanced by onboard storage of some of the compressed air stream. And the pressures are low enough that combustion shouldn't be a problem, even with H2.
Vacuum leaks are most likely to come from two sources: the end station airlocks, and the capsules themselves. Most of the tube is just Big Dumb Pipe (tm), which really shouldn't leak. And 100Pa is really not too difficult to maintain; the volume of the entire LA-SF Hyperloop tube is equivalent to a cube about 130 meters on a side.